03. Write a program to generate all the Prime numbers between '2' and 'n'

#include<iostream.h>

void prime(int n);                  //function declaration

int main()
{
    int n;                                //variable declaration
    cout<<"Please enter a valid 'n' value"<<endl;
    cin>>n;                            //reading 'n' value
    while(n<1)                       //validating 'n' value
    {
        cout<<"You have entered a invalid Number"<<endl;
        cout<<"Please enter a valid Integer"<<endl;
        cin>>n;
    }
    cout<<"serice of prime numbers upto 'n' is :"<<endl;
    prime(n);                          //calling function
    return 0;                           //successful termination
}

/* method 1...............*/

void prime(int n)                    //called function
{
    int elem;                                                //to check each element upto 'n' is whether prime or not
    int fact;                                                  //to count the number of factors for each 'elem'
    int i;                                                       //holds the factors of each 'elem' on run time
    for(elem=2;elem<=n;++elem)                 //the possibility of prime number is >= '2'
    {
        fact=0;                                              //to initialize the number of factors for each 'elem'
        for(i=1;i<=elem;++i)                         //to check the factors of each 'elem'
        {
            if(elem%i==0)                              //factor divides the element without remainder
            fact++;                                        //counts the number of factors for each 'elem'
        }
        if(fact==2)                                       //prime number has only '2' factors (1 and 'itself')

        cout<<"\n '"<<elem<<"' is a prime"; //printing the prime number

    }
}

/* Method 2............*/

void prime(int n)
{
        int elem,i;
        bool flag=;
        for(elem=2;elem<=n;++elem)
        {
                i=2;
                flag=false;
                while(!flag&&i<=elem/2)
                {
                        if(elem%i==0)
                                flag=true;
                        ++i;
                }
                if(flag==false)
                cout<<"\n '"<<elem<<"' is a prime";
        }
}